How to Determine the Probability of Ruin from Day Trading

Expected return is how much money you can expect to make if you stay in the day trading game. But it has a counterpart that is at least as important: the probability of ruin.

As long as some probability of loss exists, no matter how small, there is some probability that you can lose everything when you’re trading. How much you can lose depends on how large each trade is relative to your account, the likelihood of each trade having a loss, and the size of the losses as they occur.

Many traders who have winning trading strategies find themselves shut down because a few bad trades ruined them. Every trader has some losses, but these losses don't have to end your trading career if you know the probability of ruin and how to use it. The equation you use to calculate the probability of ruin (R) is

In this equations, A is the advantage on each trade. That’s the difference between the percentage of winning trades and the percentage of losing trades. In the expected return example discussed earlier, trades win 60 percent of the time and lose everything 40 percent of the time. In that case, the trader’s advantage would be

60% – 40% = 20%

And c is the number of trades in an account. Assume that you’re dividing the account into ten equal parts, with the plan of making ten trades today. The probability of ruin today is 1.7 percent, as shown in this equation:

Now 1.7 percent isn’t a high likelihood of ruin, but it’s not zero, either. It can happen. If your advantage is smaller, if the expected loss is larger, or if the number of trades is fewer, then the likelihood becomes even higher.

The bigger the edge and the more trades you can make, the lower your probability of ruin. Now, this model is a simplification in that it assumes that a losing trade goes to zero, and that’s not always the case. In fact, if you use stops (automatic buy and sell orders), you should never have a trade go to zero.

But you can see steady erosion in your account that will make it harder for you to make money. Hence, probability of ruin is a useful calculation that shows whether you’ll lose money in the long run.

The more trades you can make with your account, the lower your probability of ruin. That’s why money management is a key part of risk management.